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The following reaction descomposes N 2 O 5 → 2NO 2 + 1 2 O 2 . At a 25 degree centigrade the rate constant of the reaction is 5 × 1 0 - 2 sec - 1 ⁡ . The initial pressure of N 2 O 5 is 0 .2 atm . If total pressure of gaseous mixture becomes 0 .35 atm, then calculate the time of decomposition of N 2 O 5 .

Options

  1. A238.6 s e c o n d s
  2. B138.6 s e c o n d s
  3. C69.3 s e c o n d s
  4. D89.3 s e c o n d s

Correct answer

B. 138.6 s e c o n d s

Step-by-step solution

(i) The decomposition reaction is represented by Total pressure = p 0 - x + 2 x + x 2 = p 0 + 3 2 x = 0.2 a t m . or 3 x 2 = 0.35 - 0.2 = 0.15 x = 0.1 a t m Pressure of N 2 O 5 after t seconds, P = P 0 - x = 0.2 - 0.1 = 0.1 a t m Now applying first order rate law t = 2.303 k log 10 0.2 0.1 = 2.303 5 × 1 0 - 3 log 10 ⁡ 0.2 0.1 = 138.6 s e c o n d s

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